Locating the missing cards using vacant spaces
Here is an example of using vacant spaces to find a missing Queen. There is also a nice twist to the hand because we have to decide whether to finesse for an overtrick or play safe.
The more cards we know that one player has means the greater the chance that the other player has the missing ones.
Bidding after they overcall our 1NT opening
North has opened 1NT and East has bid 2♥. Now I'm going to bid 3♠ here. I'm too strong for 2♠. If I bid 2♠ North would probably pass. You could just bid 3NT on this hand as well. Anyway, I'm bidding 3♠, North bids 4♠ and that's high enough.
Play of the hand in 4♠
West leads a heart. No surprise there because East bid hearts and that looks a little ominous. Indeed it is as East wins the ♥A and returns a heart which West ruffs.
Counting the cards
West had a singleton heart, but we can use this information later on in the hand. So let's just quickly check here. North started with three hearts and I started with three hearts and West had one, a singleton. So that means East started with a six card heart suit. So let's just keep that in our head.
West now plays a diamond. So let's win the ace of diamonds and draw some trumps.
Drawing trumps
We started with a nine card spade fit and West ruffed once and follows suit once. East follows to two rounds of trumps. So West started with two and East started with two.
After we draw trumps this is the position. Remember that the ♥J is now a winner.
Here's where we can use this vacant spaces idea. We know that East started with six hearts and we know that East started with two spades. So we know about eight of East's cards. There's five cards in the East hand that we don't know about.
We know that West started with one heart and we know that West started with two spades. There's 10 cards in the West hand that we don't know about. 10 cards in the West hand we don't know about, five cards in the East hand we don't know about.
Who has the missing Queen?
Where's the ♣Q? The ♣Q is more likely to be in the hand with 10 cards that we don't know about, which is the West hand. So we've actually got two ways to play the club suit here. We could go over to the ♣A and then play the Jack letting it run round, hoping that East has got the ♣Q. Or we could play the ♣K and then a low club, finessing and hoping West has got the queen of clubs.
West is more likely to have the queen of clubs, so I could play the ♣K and then finesse West for the ♣Q. There's no guarantee that this will work, it's just playing the odds.
But if that club finesse hadn't worked, we would have lost the ace of hearts, the heart ruff, a club and a diamond. Can you see a safer way to play the hand?
End play
We can simply take our winning heart and exit with a diamond, forcing the opponents to lead to us. Now East or West, whoever wins, is going to be stuck. If they lead a club we a free finesse and if they lead a diamond or a heart we get to throw a club from hand and ruff in the dummy.
tags: #counting
